This invention relates to digital filters.
It is known to provide a decimating digital low-pass filter at the output of an analog-to-digital (A to D) converter to enable the A-to-D converter to achieve increased amplitude resolution by oversampling the analog signal (i.e., at a multiple of the Nyquist rate). In a decimating digital filter, the output sample rate is lower (e.q., 100 times lower) than the input sample rate.
Candy, "Decimation for Sigma Delta Modulation," IEEE Trans. on Comm., Jan., 1986, shows that for A-to-D converters using second order sigma delta modulation, a near optimal frequency response for the decimation filter is EQU H(f)=sin.sup.3 (.pi.Nf/f.sub.s)/sin.sup.3 (.pi.f/f.sub.s)
where N is the decimation ratio (between the input sampling rate --fs--and the output sampling rate).
Huber et al., FIR Lowpass Filter for Signal Decimation . . . , ICASSP, 1986, Tokyo, describe a decimation filter that does not require any explicit multiplication and achieves the desired response for use with a sigma delta modulator by an FIR filter followed by cascaded accumulators. Decimation is performed by a separate unit that follows the filter.
A-to-D converters are used, for example, in modems to convert the analog line signal to digital. In typical echo cancellation modems, echo cancellation and resampling are both performed in the analog domain and are followed by a relatively low-resolution analog-to-digital converter. Modems that must serve other communication schemes, e.q., frequency division multiplexing, require alternative receive filters; a multi-mode modem may be provided with multiple analog receive filters that can be program selected.